The distances traveled during equal intervals of time by a freely falling body from rest are in the ratio

Options

A. `1:2:3`
B. `1:5:9`
C. `1:3:5`
D. `sqrt1:sqrt2:sqrt3`

Answer

C

Explanation

Distance travelled by an object in a pariticular second.
`s _(t) = u + (1)/(2) g (2 t -1)`
For 1s
`s _(1) = 0 + (1)/(2) g " "...(1)`
For 2 s
`s _(2) = 0 + (1)/(2) g (4-1) `
`= (1)/(2) g xx 3 " "...(ii)`
For 3 s
`s _(3) = 0 + (1)/(2) g (6-1) = (1)/(2) g xx 5" "...(iii)`
The ratio of distance
`s _(1) : s _(2) : s _(3) (1)/(2) g : (3)/(2) g : (5)/(2) g = 1:3:5`